Question

A bag contains 5 red marbles and 4 green marbles. What is the probability of choosing a red marble then a green marble, without replacement? 1) 2572 2) 518 3) 2581 4) 2081

Answer 1

the probability of choosing a red marble then a green marble, without replacement is 5/18. Option 2 is correct.

Step-by-step explanation:

To solve this probability question, we'll go through each step of the scenario described. It consists of two separate events:

1) Choosing a red marble first.
2) Choosing a green marble second, without replacement.

First, let's find the probability of each step:

1) Probability of choosing a red marble first (Event A):
We have a total of 5 red marbles out of a total of 5 red + 4 green marbles in the bag. So, the probability of drawing a red marble first is the number of red marbles divided by the total number of marbles:


`\[ P(A) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = (5)/(5 + 4) = (5)/(9) \]`

2) Probability of choosing a green marble second (Event B):
After one red marble has been removed from the bag, we have 4 green marbles left out of a new total of 8 marbles (since no replacement was made). So, the probability of drawing a green marble next is the number of green marbles divided by the new total:


`\[ P(B|A) = \frac{\text{Number of green marbles}}{\text{New total number of marbles}} = (4)/(8) = (1)/(2)\]`

Now we need to find the combined probability of both A and B happening in sequence (choosing a red marble first AND choosing a green marble second without replacement). The combined probability is the product of the probabilities of each event:


`\[ P(A \text{ and } B) = P(A) * P(B|A) \]`

`\[ P(A \text{ and } B) = (5)/(9) * (1)/(2) \]`

Now we just multiply the two fractions:

`\[ P(A \text{ and } B) = (5)/(9) * (1)/(2) = (5 * 1)/(9 * 2) = (5)/(18) \]`

Therefore, the probability without replacement is 5/18. Option 2 is correct.